Kinematic Sensitivity Analysis of Parallel Mechanisms by Considering the Effect of Uncertainties in Passive Joints

The sensitivity of the moving platform of parallel mechanisms to the uncertainties in the design and control stages is of paramount importance. The mechanism has to be designed such that the negative effect of the foregoing errors is minimized. The latter issue has encouraged many researchers to derive and propose relevant indices being responsible for outputting a metric representing the kinetostatic performance of parallel mechanisms. Most of such indices entail severe drawbacks in the sense of leading to physically inapplicable interpretation, which was considerably alleviated by the emergence of kinematic sensitivity. Nevertheless, none of the studies heretofore has investigated the influence of the uncertainties in the passive joints on the kinetostatic performance. In other words, the assumption has always been that the aforementioned errors are negligible. This paper proposes a novel formulation for the kinematic sensitivity index, which, apart from that of the active joints, takes the effect of the uncertainties in the passive joints into account, and brings about the advantage that the mechanism can be optimized and improved in terms of kinetostatic performance, together with the workspace. The formulation, for the sake of illustration and verification, is also applied to the 4-bar linkage and 3-RPR parallel mechanisms, as well as the Tripteron robot. The results of the implementation of the proposed kinematic sensitivity index, which takes the effect of the uncertainties in the passive joints into account, show that the values associated with the case-studies considered in this paper fall within the intervals 1-2.4, 0.1-0.9 and 0.6-2.2, respectively.